docs: def flux_up(self, fluxUpBottom, emission=None):
          '''Compute downwelling radiative flux at interfaces between layers.
  
          Inputs:
  
              * fluxDownTop: flux down at top
              * emission: emission from atmospheric levels (N)
                defaults to zero if not given
  
          Returns:
  
              * vector of downwelling radiative flux between levels (N+1)
                element 0 is the flux down to the surface.
  
          '''
          if emission is None:
              emission = np.zeros_like(self.absorptivity)
          E = np.concatenate((emission, np.atleast_1d(fluxUpBottom)), axis=-1)
          #  dot product (matrix multiplication) along last axes
          return np.squeeze(matrix_multiply(self.Tup, E[..., np.newaxis]))